# 4.7: Use Scale Factor When Problem Solving

**At Grade**Created by: CK-12

**Practice**Scale Factor to Find Actual Dimensions

Lifan’s driveway has a length of 24 feet. If the scale is

In this concept, you will learn to use scale factors when problem solving.

### Scale Factor

The scale can be used to help you with scale dimensions or actual dimensions. This scale is key in problem solving.

If you look at the scale **scale factor**. The scale factor is the relationship between the scale dimension and the measurement comparison between the scale measurement of the model and the actual length. In this case the scale factor is

Let’s look at an example.

What is the scale factor if 3 inches is equal to 12 feet?

First, write the ratio.

Next, simplify the fraction.

The answer is

The scale factor is

Now let’s look at a problem where you are applying this information.

If the scale dimension is 4, then you can figure out the actual dimension. Look at this proportion:

First, put the proportion in fraction form.

Next, cross multiply to solve for

The answer is 8.

This is the actual dimension.

Let’s look at a real world problem.

The plans for a flower garden show that it is 6 inches wide on the plan. If the scale for the flower garden is

First, write the proportion.

Next, put the proportion in fraction form.

Then, cross multiply to solve for

The answer is 72.

The actual width of the flower garden is 72 inches.

### Examples

#### Example 1

Earlier, you were given a problem about Lifan and his long driveway. The scale is

First, write the proportion. Note that

Next, put the proportion in fraction form.

Then, cross multiply to solve for

Then, divide both sides by 4 to solve for

The answer is 12.

The scale dimension of Lifan’s driveway is 12 inches.

#### Example 2

Find the missing actual dimension if the scale factor is

First, write the proportion.

Next, put the proportion in fraction form.

Then, cross multiply to solve for

Then, divide both sides by 2 to solve for

The answer is 9.

The actual dimension is 9 feet.

#### Example 3

Find the missing actual dimension if the scale factor is

First, write the proportion.

Next, put the proportion in fraction form.

Then, cross multiply to solve for

The answer is 128.

The actual dimension is 128 feet.

#### Example 4

Find the missing actual dimension if the scale factor is

First, write the proportion.

Next, put the proportion in fraction form.

Then, cross multiply to solve for

Then, divide both sides by 16 to solve for

The answer is

The actual dimension is

#### Example 5

Find the missing actual dimension if the scale factor is

First, write the proportion.

Next, put the proportion in fraction form.

Then, cross multiply to solve for

The answer is 256.

The actual dimension is 256 feet.

### Review

Figure out each scale factor.

1.

2.

3.

4.

5.

6.

7.

8.

Solve each problem.

9. A rectangle has a width of 2 inches. A similar rectangle has a width of 9 inches. What scale factor could be used to convert the larger rectangle to the smaller rectangle?

10. A drawing of a man is 4 inches high. The actual man is 64 inches tall. What is the scale factor for the drawing?

11. A map has a scale of

12. A drawing of a box has dimensions that are 2 inches, 3 inches, and 5 inches. The dimensions of the actual box will be

13. A room has a length of 10 feet. Hadley is drawing a scale drawing of the room, using the scale factor

14. The distance from Anna’s room to the kitchen is 15 meters. Anna is making a diagram of her house using the scale factor of

15. On a map of Cameron’s town, his house is 9 inches from his school. If the scale of the map is

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.7.

### Resources

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Actual Dimension

The actual dimensions are the real–life measures of the object or building.Proportion

A proportion is an equation that shows two equivalent ratios.Scale Dimension

A scale dimension is the measurement used to represent actual dimensions in a drawing or on a map.### Image Attributions

In this concept, you will learn to use scale factors when problem solving.

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